The aim of this paper is the formulation and the study of a prey-predator model
to describe fish and plankton population dynamics, with three developmental stages of the
fish population (larva, juvenile and adult). First, we develop a mathematical model based on
the ODEs, describing the dynamics of the various classes for the fish population depending
on the plankton in a general framework. Then, we are interested in the model in the case
of a trophic chain predation for the fish population. Finally, we continue our study through
numerical simulations of the model in different fishing areas. The obtained numerical results
confirm the mathematical analysis and allow us to have an idea on the development of the
fish population in a fishing area.

Populations dynamics, global stability, fishing effort, prey-predator model, ODEs system